As a bright gamma-ray source , 3C 66A is of great interest to the high-energy astrophysics community , having a potential for placing cosmological constraints on models for the extragalactic background light ( EBL ) and the processes which contribute to this photon field . No firm spectroscopic redshift measurement has been possible for this blazar due to a lack of intrinsic emission and absorption features in optical spectra . We present new far-ultraviolet spectra from the Hubble Space Telescope/Cosmic Origins Spectrograph ( HST/COS ) of the BL Lac object 3C 66A covering the wavelength range 1132 to 1800 Å . The data show a smooth continuum with intergalactic medium absorption features which can be used to place a firm lower limit on the blazar redshift of z \geq 0.3347 . An upper limit is set by statistically treating the non-detection of additional absorbers beyond z = 0.3347 , indicating a redshift of less than 0.41 at 99 % confidence and ruling out z \geq 0.444 at 99.9 % confidence . We conclude by showing how the redshift limits derived from the COS spectra remove the potential for this gamma-ray emitting blazar to place an upper limit on the flux of the EBL using high energy data from a flare in October of 2009 .